This invention is directed to a process for moiré-free halftoning color documents using combinations of non-orthogonal cluster screens.
With the advent of inexpensive digital color printers, methods and systems of color digital halftoning have become increasingly important. It is well understood that most digital color printers operate in a binary mode, i.e., for each color separation, a corresponding color spot is either printed or not printed at a specified location or pixel. Digital halftoning controls the printing of color spots, where spatially averaging the printed color spots of all the color separations provides the illusion of the required continuous color tones.
The most common halftone technique is screening, which compares the required continuous color tone level of each pixel for each color separation with one of several predetermined threshold levels. The predetermined threshold levels are stored in a halftone screen. If the required color tone level is darker than the threshold halftone level, a color spot is printed at the specified pixel. Otherwise the color spot is not printed. It is understood in the art that the distribution of printed pixels depends on the design of the halftone screen. For cluster halftone screens, all printed pixels are grouped into one or more clusters. If a cluster-halftone screen only generates a single cluster, it is referred to as a single-cell halftone screen or a single-cell halftone dot. Alternatively, halftone screens may be dual-dot, tri-dot, quad-dot, or the like.
Halftone screens are typically two-dimensional threshold arrays and are relatively small in comparison to the overall image or document to be printed. Therefore, the screening process uses an identical halftone screen repeated for each color separation in a manner similar to tiling. The output of the screening process, using a single-cell halftone dot, includes a binary pattern of multiple small “dots”, which are regularly spaced and is determined by the size and the shape of the halftone screen. In other words, the screening output, as a two-dimensionally repeated pattern, possesses two fundamental spatial frequencies, which are completely defined by the geometry of the halftone screen.
While halftoning is often described in terms of the halftone dots, it should be appreciated that halftone dots can also posses shapes ranging from rectangles, squares, lines, and the like. Various digital halftone screens having different shapes and angles are described in “An Optimum Algorithm for Halftone Generation for Displays and Hard Copies”, by T. M. Holladay, Proc. Soc. for Information Display, 21, p. 185 (1980).
A common problem that arises in digital color halftoning is the manifestation of moiré patterns. Moiré patterns are undesirable interference patterns that occur when two or more color halftone separations are printed over each other. Since color mixing during the printing process is a non-linear process, frequency components other than the fundamental frequencies of the two or more color halftone separations can occur in the final printout. For example, if an identical halftone screen is used for two color separations, theoretically, there should be no moiré patterns. However, any slight misalignment between the two color halftone separations occurring from an angular difference and/or a scalar difference will result in two slightly different fundamental frequencies, which will be visibly evident as a very pronounced moiré interference pattern in the output. To avoid, for example, two-color moiré patterns due to misalignment, or for other reasons, different halftone screens are commonly used for different color separations, where the fundamental frequencies of the different halftone screens are separated by relatively large angles. Therefore, the frequency difference between any two fundamental frequencies of the different screens will be large enough so that no visibly noticeable moiré patterns are produced.
In selecting different halftone screens, for example, for three color separations, it is desirable to avoid any two-color moiré as well as any three-color moiré. It is well known that in the traditional printing industry that three halftone screens, which are square in shape and identical, can be placed at 15, 45, and 75, degrees, respectively, from a point of origin, to provide the classical three-color moiré-free solution. This is described in “Principles of Color Reproduction”, by J. A. G. Yule, John Wiley & Sons. N.Y. 1967.
However, for digital halftoning, the freedom to rotate a halftone screen is limited by the raster structure, which defines the position of each pixel. Since tan(15°) and tan(75°) are irrational numbers, rotating a halftone screen to 15° or 75° cannot be exactly implemented in digital halftoning. To this end, some methods have been proposed to provide approximate instead of exact moiré-free solutions. For example, in U.S. Pat. Nos. 5,323,245 and 5,583,660, this problem is approached by using a combination of two or more perpendicular, unequal frequency screen patterns and non-perpendicular, equal frequency non-conventional screen patterns. However, all these approximate solutions result in some halftone dots having centers that do not lie directly on addressable points, or on the pixel positions defined by the raster structure. Therefore, the shape and center location varies from one halftone dot to another. Consequently, additional interference or moiré between the screen frequencies and the raster frequency can occur. In another approach, U.S. Pat. No. 5,371,612 discloses a moiré prevention method to determine screen angles and sizes that is usable solely for square-shaped, halftone screens.
U.S. Pat. No. 6,798,539 to Wang et al., discloses methods for using single-cell, non-orthogonal cluster screens to satisfy the moiré-free conditions for color halftoning. The disclosure also provides methods that combine single-cell non-orthogonal cluster screens and line screens for moiré-free color halftoning. Particularly, the selection of these single-cell halftone screens is determined by satisfying moiré-free conditions provided in the respective spatial or frequency equations. U.S. Pat. No. 6,798,539 to Wang et al. provides a background basis for the disclosure as taught in the specification which follows below, and as such is hereby incorporated in its entirety for its teachings.
As provided herein, there is supplied teachings to systems and methods that combine single-cell non-orthogonal cluster screens in different color separations for moiré-free color halftoning.
Disclosed in embodiments herein is a method for generating a plurality of non-orthogonal halftone screens for moiré free color halftoning. The method defining a first color halftone screen having a first fundamental frequency vector Vc1 and second fundamental frequency vector Vc2. The method also defining a second color halftone screen having a first fundamental frequency vector Vm1 and second fundamental frequency vector Vm2 and, adjusting the values of the fundamental frequency vectors to identify combinations that satisfy the following:
                    V                  c          ⁢                                          ⁢          2                    +              V                  m          ⁢                                          ⁢          1                      =                  -                  1          2                    ⁢              V                  c          ⁢                                          ⁢          1                      ,          ⁢                    V                  c          ⁢                                          ⁢          1                    -              V                  m          ⁢                                          ⁢          2                      =                  -                  1          2                    ⁢                        V                      m            ⁢                                                  ⁢            1                          .            
Also disclosed in embodiments herein is method for generating a plurality of non-orthogonal halftone screens for moiré free color halftoning. The method defining a first color halftone screen having a first fundamental frequency vector Vc1 and second fundamental frequency vector Vc2. The method also defining a second color halftone screen having a first fundamental frequency vector Vm1 and second fundamental frequency vector Vm2 and, adjusting the values of the fundamental frequency vectors to identify combinations that satisfy where the sum of the first color halftone screen second fundamental frequency vector Vc2 and the second color halftone screen first fundamental frequency vector Vm1 equate to a function of the first color halftone screen first fundamental frequency vector Vc1 while also satisfying where the difference of the second color halftone screen second fundamental frequency vector Vm2 taken from the first color halftone screen first fundamental frequency vector Vc1 equates to a function of the second color halftone screen first fundamental frequency vector Vm1.